Density functional theory guided Monte Carlo simulations: application to melting of Na13

We present a density functional theory (DFT) based Monte Carlo simulation method in which a simple energy function gets fitted on-the-fly to DFT energies and gradients. The fitness of the energy function gets tested periodically using the classical importance function technique [R. Iftimie, D. Salahub, D. Wei, and J. Schofield, J. Chem. Phys. 113, 4852 (2000)]. The function is updated to fit the DFT energies and gradients of the most recent structures visited whenever it fails to achieve a preset accuracy. In this way, we effectively break down the problem of fitting the entire potential energy surface (PES) into many easier problems, which are to fit small local regions of the PES. We used the scaled Morse potential empirical function to guide a DFT Monte Carlo simulation of Na(13) at various temperatures. The use of empirical function guide produced a computational speed-up of about 7 in our test system without affecting the quality of the results.